This agent-based financial market model is a generalization of the model of Westerhoff (The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies) by traders who are allowed to have different investment horizons as introduced by Demary (Who Does a Currency Transaction Tax Harm More: Short-Term Speculators or Long-Term Investors?). Our research goals are, first, to study what consequences the introduction of heterogeneous investment horizons has for agent-based financial market models, and second, how effective transaction taxes are in stabilizing financial markets. Numerical simulations reveal that under sufficiently small tax rates traders abstain from short-term trading in favour of longer investment horizons. This change in behavior leads to less volatility and less mispricings. When the tax rate exceeds a certain threshold, however, mispricings increase as also found in Westerhoff (Heterogeneous Traders and the Tobin Tax and The Use of Agent-Based Financial Market Models to Test the Effectiveness of Regulatory Policies). This emergent property is due to the fact that taxation reduces short-term fluctuations and causes longer lasting trends in the exchange rate. As a result, the longer term fundamentalist trading rule becomes unpopular in favor of the longer term trend-chasing rule.